MEASUREMENT OF IONIZING RADIATIONS 167 



advantages and, in special cases, offers also the possibility of clarifying 

 particular aspects of the action of the radiation. 



In principle, if the source is present in uniform concentration, C, in 

 homogeneously absorbing media, the dose (ergs per gram), at points in 

 the medium removed from the surface by distances efjual to or greater 

 than the range of the fastest ionizing particle, is equal to the /3-ray energy 

 emitted by the radioelement contained in 1 g of the medium. 



The total dose D^ due to the complete disintegration in situ of the 

 radioelement is then given by 



D, = K,C ergs/g (15) 



where K^ = 73OOE0T, T is the half-life of the isotope in days, and E^ 

 is the average /3-ray energy in mega electron volts per disintegration 

 (Marinelli, 1942; Marinelli, Brinckerhoff, and Hine, 1947; Marinelli, 

 Quimby, and Hine, 1948; Marinelli, 1949; Failla, Rossi, Clark, and Baily, 

 1947). The term Kg gives the dose directly in ergs per gram for each 

 microcurie completely destroyed within 1 g of medium.^" 



From this formula others can be easily derived. Thus for any interval 

 of time t the dose d^{t) is proportional to that fraction jd of atoms dis- 

 integrated during that time, namely, 



d^) = Dfffd = Dffil - e-o.693*/r) (16) 



This equation can be conveniently written as 



d& = 5060EiiC ergs/g/day (17) 



when the half-life of the isotope is greater than 35 days, or 



d^ = 211 EpC ergs/g/hr (18) 



when the half-life of the isotope is greater than 35 hr, since the value of dp 

 will then be correct to better than 1 per cent. For the convenience of 

 the reader, E^ and T pertaining to some biologically useful isotopes are 

 given in Table 2-2. 



It should be realized immediately that these formulas are of very 

 limited value in the estimation of doses resulting from the irradiation of 

 small organisms in vessels of dimensions comparable to the range of the 

 fastest ^ particle, in small organs of laboratory animals, or in systems 

 exhibiting "spotty" distributions. It should be realized also that it is 

 impossible to give in concise form corrections applicable to the numerous 

 conditions of irradiation that are apt to be applied in practice. Several 

 references are available in the literature, and the reader is referred to 



'" For systems in which the isotope is excreted, the "effective" half-life, Teti, in the 

 system should be used instead of T. For exponential excretion, dC/dT = —\bC, 

 Teit = TTb/iT - Tb), where Tb = 0.693/X6 and T is the physical half-life of the 

 isotope. 



